Chromatography is a dynamic technique for separation of molecules, both analytically and in preparative scale, using gas or liquid as the mobile phase. For separation of proteins and polypeptides, liquid chromatography (LC) can be used in various modes such as, e.g., ion-exchange, reversed phase, hydrophobic interaction, affinity, and metal chelate chromatography, depending on the nature and ligands of the stationary phase. Ion-exchange chromatography primarily separates proteins based on their overall and/or local difference in charge, reversed phase and hydrophobic interaction chromatography separate proteins based on hydrophobicity of the proteins and polypeptides, while affinity chromatography (and many other modes of chromatography) separate proteins and polypeptides based on various attracting and repelling forces, including hydrogen binding, van der Waals, ionic and hydrophobic forces.
In analytical LC, loading of the chromatographic column is usually low to obtain the best possible separation of the distinct molecules present in the sample, and various elution gradients and modifiers are applied to achieve maximum resolution. In preparative LC, column loading is usually high to optimize productivity and process economy, and the separation procedure is designed to obtain optimal purity and yield of the target protein or polypeptide. Gradients and modifiers are usually applied in the most simplistic way possible to obtain the purity and yield desired. The nature of gradients in LC is linked to the mode of operation, e.g. salt and/or pH in ion-exchange chromatography, organic solvent in reversed phase chromatography, etc.
For many years, there has been a desire to adequately describe the very complex LC separation process using mathematical models for simulation of chromatographic separation. Key elements in such mathematical models include the adsorption isotherm describing solute equilibrium between the stationary and mobile phase, the overall mass balance of the chromatographic system, and an expression describing mass transfer from the mobile to the stationary phase (Perry and Green, Perry's Chemical Engineers' Handbook, Chap. 16, 7th Ed., McGraw-Hill, New York, 1997). The most recognized and applied adsorption isotherms today are those developed by Langmuir, J. Am. Chem. Soc. 40 (1918) 1361 (Langmuir isotherms) and Brooks and Cramer, AlChE J. 38 (1992) 1969-1978 (steric mass action (SMA) isotherms), and various derived expressions hereof for reversed phase and hydrophobic interaction chromatography and for ion-exchange chromatography, respectively.
Modelling has been applied to ion-exchange chromatography model systems (Karlsson et al., J. Chromatogr. A 1055 (2004) 29-39), hydrophobic interaction chromatography model systems (Jakobsson et al., J. Chromatogr. A 1099 (2005) 157-166), pseudo-affinity chromatography model system (Zhang and Sun, J. Chromatogr. A 957 (2002) 89-97, and reversed phase chromatography model system (Liu et al., Biotechnol. Prog. 18 (2002) 796-806). The latter publication described modelling of an artificial mixture of recombinant human, porcine, and human analogue insulin, and Wiesel et al. (J. Chromatogr. A 1006 (2003) 101-120) have published a modelling work with ion-exchange chromatography using an unspecified bioactive substance. Usually, however, research and verification of mathematical models are typically performed on model and non-biopharmaceutical protein mixtures, e.g. chymotrypsinogen and cytochrome c (Brooks and Cramer, AlChE J. 38 (1992) 1969-1978) and BSA (Chen et al., J. Chromatogr. A 1012 (2003) 1-10 and Lim et al., Biochem. Eng. J. 25 (2005) 125-140), and thus may not be applicable to more complex protein mixtures.
Also, while commercial programs of various quality and validity for simulation of separation processes exist, e.g. Aspentech in U.S. Pat. No. 5,666,297, all polypeptide and system specific parameters, such as the steric factor σ, the characteristic charge v, and the equilibrium constant K in the e.g. the SMA isotherm description and mass transfer coefficients, basically must be determined separately for each component in the mixture. Determination of peptide specific parameters, however, usually requires pure gram-amounts of each component in the mixture. High through-put screening (HTS) techniques in ion-exchange batch adsorption mode have recently been applied in an effort to minimize consumption of pure protein for modelling (see, e.g., Rege et al., Sep. Sci Technol. 38 (2003) 1499-1517, for displacement chromatography predictions).
Accordingly, a need still exists for a simple and adequate method for simulation and modelling of chromatographic separation of polypeptide mixtures, especially where the target protein and one or more impurities are related.